If you are using leftover, cooked white rice, skip this step and go to Step 2. In a covered saucepan on the stove top, bring 2 cups of water to a boil. When the water reaches a full boil, stir in the rice. Stir to bottom of pan a few times to make sure all rice is moistened and not sticking on the bottom of pan in lumps. Return water to a boil. Reduce heat to a very low simmer, place lid on pan and simmer for 20-minutes.
Place cooked rice a in large bowl. Set aside until needed.
Scramble eggs in skillet on stove top with 1 Tbsp of butter. After eggs are cooked, chop the scrambled eggs into pea size bits with spatula.
Stir the chopped scrambled eggs into the bowl of cooked rice along with the thawed peas and carrots and diced white onion. Stir until mixed uniformly.
Melt 2 Tbsp of butter over medium heat in a large skillet on the stove top.
When the butter is melted and heated to sizzling, add the rice mixture to the skillet. Stir and saute the rice mixture for a minute or two.
Mix the soy sauce with sesame oil in a cup and sprinkle evenly over frying rice mixture in skillet as it cooks.
Saute rice mixture for 6 to 8 minutes, stirring and turning frequently with a spatula until mixture is lightly browned.
When done, season with ground white pepper and table salt to taste. Remove from heat.
Place in large serving bowl and garnish top with diced green onions.